Question

question 3
write the equation of a line through (-5,1), parallel to $y = -\frac{1}{5}x + 1$
$y = \square x + \square$
question 4
write the equation of a line through (4,1), perpendicular to $y = 4x$
$y = \square x + \square$

Explanation:

Question 3

Step1: Identify parallel slope

Parallel lines have equal slopes. The given line is $y = -\frac{1}{5}x + 1$, so the slope $m = -\frac{1}{5}$.

Step2: Solve for y-intercept b

Use point $(-5,1)$ in $y = mx + b$:
$1 = -\frac{1}{5}(-5) + b$
$1 = 1 + b$
$b = 1 - 1 = 0$

Question 4

Step1: Identify perpendicular slope

Perpendicular slopes are negative reciprocals. Given line $y=4x$ has slope $4$, so new slope $m = -\frac{1}{4}$.

Step2: Solve for y-intercept b

Use point $(4,1)$ in $y = mx + b$:
$1 = -\frac{1}{4}(4) + b$
$1 = -1 + b$
$b = 1 + 1 = 2$

Answer:

Question 3: $y = -\frac{1}{5}x + 0$
Question 4: $y = -\frac{1}{4}x + 2$